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SUMMARY:Recent Results on Multiply Monotone Radial Functions - Martin Buhm
 ann (Justus-Liebig University\, Giessen\, Germany)
DTSTART:20180305T150000Z
DTEND:20180305T160000Z
UID:TALK100939@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:The purpose of this talk is to establish new results on interp
 olation\nto continuous functions of multiple variables. For this\, radial 
 basis function interpolation is most useful\, as it provides always regula
 r\, indeed positive definite or conditionally positive definite collocatio
 n matrices\, independent of the spatial dimension and the geometry of the 
 data points we wish to work with.\n\nThese interpolants are used for examp
 le to solve partial differential equations by collocation.\n\nSpecifically
 \, we aim to classify radial basis and other functions that are useful for
  scattered data interpolation from vector spaces spanned by translates of 
 basis functions (kernels) in any (high) dimensional space\, and to this en
 d we study so-called multiply monotonic functions. We collect special prop
 erties of such multiply monotonic functions\, generalise them and find lar
 ger classes than the well known completely monotone functions for multivar
 iate interpolation. Furthermore\, we generalise other results recently est
 ablished for completely monotone functions to this class of functions. (Jo
 int work with Janin Jäger.)
LOCATION:MR 5
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